Details

sample62.0ms

Algorithm

intervals

Results

29.0ms	261×	body	80	valid
3.0ms	4×	body	1280	valid
3.0ms	6×	body	640	valid
1.0ms	2×	body	320	valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (173.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	95	29
3	207	29
4	499	28
5	1209	28
6	4807	28
done	5000	28

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite9.4s

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
141×	`prod-diff`
130×	`associate-r`
123×	`exp-sum`
72×	`add-cube-cbrt`
66×	`unpow-prod-down`
50×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
46×	`difference-of-squares`
35×	`distribute-lft-out--`
23×	`cos-sum`
20×	`times-frac`
11×	`sqr-pow`
9×	`pow1`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-l`
5×	`neg-mul-1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-*r/` `div-inv`
2×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `exp-diff` `pow-exp` `flip-+` `distribute-lft-out` `associate--r-`

Counts

4 → 224

Calls

4 calls:

19.0ms	(* K (+ m n))
9.2s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
75.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
61.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* K (+ m n))
555.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
397.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
85.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.8s

Counts

236 → 236

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	629	9112
1	1187	7956
2	2476	7241
done	5000	6804

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize36.0ms

Local error

Found 2 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`prod-diff`
6×	`unpow-prod-down`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `pow-unpow` `fma-neg` `difference-of-squares`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `times-frac` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

2 → 50

Calls

2 calls:

8.0ms	(- l (fabs (- m n)))
120.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series415.0ms

Counts

2 → 6

Calls

2 calls:

20.0ms	(- l (fabs (- m n)))
394.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.4s

Counts

56 → 56

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	132	935
1	273	747
2	574	641
3	1649	581
done	5000	564

prune242.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize69.0ms

Local error

Found 4 expressions with local error:

14.9b	(cbrt (/ (* K (+ m n)) 2.0))
14.9b	(cbrt (/ (* K (+ m n)) 2.0))
32.1b	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
32.8b	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

rewrite335.0ms

Algorithm

rewrite-expression-head

Rules

156×	`prod-diff`
102×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
98×	`cbrt-prod`
80×	`cos-sum` `sin-sum`
60×	`unpow-prod-down` `cube-prod`
42×	`times-frac`
14×	`div-inv`
6×	`cube-mult` `unpow3` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `cbrt-div` `pow1/3`
1×	`cos-diff` `sin-diff`

Counts

4 → 216

Calls

4 calls:

11.0ms	(cbrt (/ (* K (+ m n)) 2.0))
13.0ms	(cbrt (/ (* K (+ m n)) 2.0))
116.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
180.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

series886.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(cbrt (/ (* K (+ m n)) 2.0))
278.0ms	(cbrt (/ (* K (+ m n)) 2.0))
173.0ms	(cos (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))
206.0ms	(sin (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M))

simplify3.3s

Counts

228 → 228

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	493	14384
1	793	8056
2	1186	6156
3	2611	5792
done	5001	5152

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.6b	(cbrt (pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3))
0.6b	(pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3)
32.2b	(cos (fma K (/ (+ m n) 2.0) (- M)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`cbrt-prod` `add-cube-cbrt` `unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `difference-of-squares`
1×	`cos-sum` `times-frac` `pow1/3` `rem-cbrt-cube` `fma-udef` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 80

Calls

4 calls:

77.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
3.0ms	(cbrt (pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3))
4.0ms	(pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3)
3.0ms	(cos (fma K (/ (+ m n) 2.0) (- M)))

series811.0ms

Counts

4 → 12

Calls

4 calls:

408.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
107.0ms	(cbrt (pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3))
189.0ms	(pow (cos (fma K (/ (+ m n) 2.0) (- M))) 3)
105.0ms	(cos (fma K (/ (+ m n) 2.0) (- M)))

simplify3.0s

Counts

92 → 92

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	146	1556
1	297	1352
2	666	1220
3	2841	1211
done	5000	1202

prune495.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

regimes324.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
done	21	18

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.8s	8086×	body	80	valid
114.0ms	124×	body	1280	valid
82.0ms	142×	body	640	valid
42.0ms	106×	body	320	valid
13.0ms	47×	body	160	valid
1.0ms	1×	body	2560	valid